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Book Review: Fearful Symmetry: Is God a Geometer?

“The reason for trying to understand the universe isn’t that we thereby blunder into a new material for coating non-stick frying pans. It’s that we gain insight into our place in the scheme of things, and of just how wonderful and unexpected that scheme can be. The aim of science is not just the manufacture of new toys: it’s the enrichment of the human spirit.”

Fearful Symmetry: Is God a Geometer? by Ian Stewart and Martin Golubitsky is a popular science book from the early 90’s on the subject of symmetry, with an emphasis on the fascinating phenomenon of symmetry breaking. The authors take the reader on an idiosyncratic tour of this subject, discussing cosmology, crystallography, and biology, including, for example, detailed discussions of the Couette-Taylor fluid system, animal gaits, and embryology. Throughout this book is also contained a sprinkling of sage discussion on the philosophy of science, as the opening quote attests to.

There are many popular books in existence on the topic of symmetry; what makes this book stand out is that the authors have assumed a bit of intelligence on behalf of the reader and this allows Fearful Symmetry to be more sophisticated than your average pop sci book.

However, as a physics student, I was disappointed by what was omitted in the discussion of the standard model (SM) of particle physics. The authors did, to their credit, emphasis the fundamental importance of symmetries in the SM—they even explicitely named the SU(3) gauge symmetry of quantum chromodynamics—and they also mentioned that the electroweak symmetry breaks at low energies, which results in the apparently distinct electromagnetic and weak force. Unfortunately though, there was no mention of the role of symmetry breaking in giving masses to the W and Z bosons and all of the fundamental fermions—a process called the Higg’s mechanism, which is responsible for the weakness of the weak force and the mass of electrons. This, in my biased opinion, is one of the most—if not the most—important examples of symmetry breaking in nature, so it is a shame that it wasn’t included.

Another thing that annoyed me was the statement of the purported mystery that all particles of the same type are identical; this is indeed a deep empirical fact that needs explaining, but it’s not a mystery in the context of the very successful field-based theories of modern particle physics: all particles of the same type are identical (up to a minus sign) because they arise from the same underlying field. There were also some out-dated references to the promise of grand unified theories and string theory, but that’s only because the book was written two decades ago.

Admittedly, I’m being pedantic. It’s only because this book is more intellectual and goes deeper than most non-technical accounts that I hold it to high standards, so this criticism should be taken as a compliment to the rest of the book. Overall, the authors do a good job of explaining the unassuming ubiquity of symmetry and symmetry breaking in the real world, which makes for some fairly interesting reading on an important topic.